department head vs top dog

department head and top dog both are nouns.

Word	Noun	Adjective	Verb	Adverb
department head	Yes	No	No	No
top dog	Yes	No	No	No

As nouns, top dog is a hypernym of department head; that is, top dog is a word with a broader meaning than department head:

Other hypernyms of department head include chief, head.

department head (noun)	top dog (noun)
the head of a department	a person who is in charge